The obligation of "Mipeneh Seba Takum Ve’hadarta Peneh Zaken" requires one to stand as an expression of honor when his father or Rabbi walks into the room. (This is also required when an elderly person walks into the room; this applies to people aged 70 and above, according to the Shulhan Aruch, or 60 and above, according to the Ben Ish Hai.) However, the Rama (Rav Moshe Isserles of Cracow, 1525-1572), in Yoreh De’a (376:2), rules that this requirement does not apply to a person in mourning. If a person’s father or Rabbi walks into the room while he observes Shiba, he does not have to stand to show honor. The reason is that the father or Rabbi presumably foregoes on this honor in consideration of the individual’s plight. Since he is in mourning, there is no expectation that he should rise to give honor.
This exemption does not apply to our state of mourning on Tisha B’Ab. If a person’s Rabbi or father walks into the room on Tisha B’Ab, he must stand, despite the fact that we are all considered mourners on this day. The exemption for a mourner stems from the fact that the mourner is in an especially difficult condition, whereas his father or Rabbi is not, and it can therefore be assumed that there is no expectation of honor. However, on Tisha B’Ab, we are all in a state of mourning, and thus no person is experiencing especially difficult hardship beyond that which his father or Rabbi experiences. Hence, it cannot be presumed that the obligation of honor is waived, and thus one must stand for his Rabbi or father on Tisha B’Ab.
Summary: Although a mourner is exempt from the obligation to stand as a show of honor when his father or Rabbi enters the room, we are required to stand in their honor on Tisha B’Ab, despite the fact that we are all considered mourners.